He analyzes the psychological process needed to obtain the concept of number and then tries to build up a systematical theory on this analysis.

To achieve this he uses several methods and concepts taken from his teachers.

From Weierstrass he derives the idea that we generate the concept of number by counting a certain collection of objects.

From Brentano and Stumpf he takes over the distinction between proper and improper presenting.

In an example Husserl explains this in the following way: if you are standing in front of a house, you have a proper, direct presentation of that house, but if you are looking for it and ask for directions, then these directions (e.g. the house on the corner of this and that street) are an indirect, improper presentation.

In other words, you can have a proper presentation of an object if it is actually present, and an improper (or symbolic as he also calls it) if you only can indicate that object through signs, symbols, etc.

Another important element that Husserl took over from Brentano is intentionality, the notion that the main characteristic of consciousness is that it is always intentional. While often simplistically summarised as "aboutness" or the relationship between mental acts and the external world, Brentano defined it as the main characteristic of mental phenomena, by which they could be distinguished from physical phenomena.

Some years after the publication of his main work, the Logische Untersuchungen (Logical Investigations; 1900-1901) Husserl made some key conceptual elaborations which led him to assert that in order to study the structure of consciousness, one would have to distinguish between the act of consciousness and the phenomena at which it is directed (the object-in-itself, transcendent to consciousness).

Knowledge of essences would only be possible by "bracketing" all assumptions about the existence of an external world.

He called this procedure epoché.

Husserl then started to concentrate on the ideal, essential structures of consciousness.

Husserl proposed that the world of objects and ways in which we direct ourselves toward and perceive those objects is normally conceived of in what he called the "natural standpoint", which is characterized by a belief that objects materially exist and exhibit properties that we see as emanating from them.

Husserl proposed a radical new phenomenological way of looking at objects by examining how we in our many ways of being intentionally directed toward them, actually "constitute" them (to be distinguished from materially "creating objects or objects" .

Husserl tries new methods of bringing his readers to understand the importance of phenomenology to scientific observation: specifically he refers to psychology) and what he means for "bracketing natural attitude".

The Crisis of the European Sciences is Husserl's unfinished work that deals most directly with these issues. In it, Husserl for the first time attempts a historical overview of the development of Western philosophy and science, emphasizing the challenges presented by their increasingly (one-sidedly) empirical and naturalistic orientation.

Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy -- First Book: General Introduction to a Pure Phenomenology, 1982 [1913]. Kersten, F., trans. The Hague: Nijhoff.

Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy - Second Book: Studies in the Phenomenology of Constitution, 1989. R. Rojcewicz and A. Schuwer, translators. Dordrecht: Kluwer.

Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy - Third Book: Phenomenology and the Foundations of the Sciences, 1980, Klein, T. E., and Pohl, W. E., translators. Dordrecht: Kluwer.

--------, 1962 (French), 1976 (English). Introduction to Husserl's The Origin of Geometry. Includes Derrida's translation of Appendix III of Husserl's 1936 The Crisis of European Sciences and Transcendental Phenomenology.